Hi I have the following matrix

A=[a_11 a_12 a_13 1; a_21 a_22 a_23 1; . . . a_n1 a_n2 a_n3 1]

I have seen that when some of a_ij are big for instance in the order of 200 , then condition number is also big.

I would like to know is it possible to show it theoretically.

Is it possible to find a lower bound for this problem?

Regards,

Reza